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Bayesian statistics is a branch of statistics that interprets probability as a measure of belief or certainty rather than a frequency of occurrence. This approach is named after Thomas Bayes, who formulated Bayes' theorem in the 18th century. Bayesian statistics uses Bayes' theorem to update the probability of a hypothesis as more evidence or information becomes available.
Key Concepts
Bayes' Theorem
Bayes' theorem is the foundation of Bayesian statistics. It describes how to update the probabilities of hypotheses when given evidence. The theorem is expressed as:
[ P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)} ]
Where:
( P(H|E) ) is the posterior probability, the probability of hypothesis ( H ) given the evidence ( E ).
( P(E|H) ) is the likelihood, the probability of evidence ( E ) given that ( H ) is true.
( P(H) ) is the prior probability, the initial probability of ( H ) before seeing the evidence.
( P(E) ) is the marginal likelihood, the total probability of the evidence.
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Bayesian statistics - Wikipedia
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